Middle Tennessee’s housing market is improving, according to a pair of reports issued today.

Housing starts soared in the final three months of 2012 compared to the same period a year earlier, Metrostudy said in its latest quarterly report. And asking home prices and rents showed healthy gains in January, Trulia reported in its monthly Monitor reports.

In the fourth quarter, homebuilders broke ground on 1,152 units in the eight Middle Tennessee counties that Metrostudy surveys. That’s up 62 percent from the year-ago quarter.

New-home closings in the October-December quarter also were higher, rising from 1,002 in 2011 to 1,196 last year.

The only downside: Tightening inventory. Builders had just a 1.9-month supply of completed homes on hand, less than half from a year ago, Metrostudy said.

Tight supply and rising demand have pushed home sellers’ asking prices and rents higher in the Nashville region, said Trulia, a real-estate research and listing firm.

Nashville rents were 6.7 percent higher last month than a year earlier, while asking prices rose by 4.8 percent over the past year, the company said.

That combination bodes well for the Middle Tennessee housing market, said Jason Brown, Metrostudy’s Nashville director.

“Barring any major economic setbacks, these factors combined with continued steady employment growth, the area’s lack of new home inventory and home values increasing, Nashville should expect to see upward movement in the new home market through 2013,” he said.